I am trying to understand the article "Realization spaces for tropical fans" https://arxiv.org/pdf/0909.4582.pdf by Eric Katz and Sam Payne.
Let $X\subset T$ be a subvariety of the torus. The topicalization Trop$(X)$ with respect to the trivial valuation is the set $v\in N_\mathbb{R}$ such that the initial degeneration in$_v(X)$ in $T$ is nonempty.
Can someone explain how the initial degeneration is defined in this case or do someone has a good source?